EduSahara™ Worksheet

Question 1

1.

The angles of depression of two boats from the top of a cliff 100 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

179.74 m
(ii)

140.74 m
(iii)

157.74 m
(iv)

170.74 m
(v)

132.74 m

Question 2

2.

The angles of depression of two boats from the top of a cliff 200 m high are 30° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

214.94 m
(ii)

230.94 m
(iii)

246.94 m
(iv)

237.94 m
(v)

217.94 m

Question 3

3.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
45°
.
If the height of the
chimney
is
130 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

130

√

2

m
(ii)

260

m
(iii)

65

√

12

m
(iv)

260

√

3

m
(v)

130

m

Question 4

4.

From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 45° and the angle of depression of its foot is 30°. Find the height of the cable tower.

(i)

49.64 m
(ii)

54.64 m
(iii)

51.64 m
(iv)

59.64 m
(v)

57.64 m

Question 5

5.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of depression ?

(i)

∠g
(ii)

∠d
(iii)

∠e
(iv)

∠f

Question 6

6.

A man in a boat rowing away from a lighthouse 70 m high, takes 4.5 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.

(i)

1.11 m/sec
(ii)

2.11 m/sec
(iii)

0.11 m/sec
(iv)

7.11 m/sec
(v)

8.11 m/sec

Question 7

7.

Two boys are on opposite sides of a tower of 150 m height. They measure the angle of elevation of the top of the tower as 60° and 45° respectively. Find the distance between the two boys.

(i)

(

50

√

3

+

150

)

m
(ii)

(

75

√

2

+

75

√

6

)

m
(iii)

(

−

15000

)

m
(iv)

(

50

√

18

+

150

√

6

)

m
(v)

(

−

2

−

√

3

)

m

Question 8

8.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
45°
.
If the distance between the point and the top of the
tower
is
200 m
,
find the height of the
tower
.

(i)

100

√

2

m
(ii)

200

√

3

m
(iii)

50

√

12

m
(iv)

100

m
(v)

200

m

Question 9

9.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 60° with the ground. The top of the tree touches the ground at a distance of 20 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

79.64 m
(ii)

71.64 m
(iii)

74.64 m
(iv)

77.64 m
(v)

69.64 m

Question 10

10.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 45°. If the height of the flag staff is 9 m, find the height of the building .

(i)

17.29 m
(ii)

12.29 m
(iii)

15.29 m
(iv)

7.29 m
(v)

9.29 m

Question 11

11.

Two poles of equal height are standing opposite to each other on either side of a road which is 20 m wide. From a point between them on the road, the angles of elevation of the top of the poles are 30° and 60° respectively. Find the height of each pole and the distances of the point from the two poles .

(i)
height =

10.66 m

, distances away =

7 m

,

17 m
(ii)
height =

8.66 m

, distances away =

5 m

,

15 m
(iii)
height =

6.66 m

, distances away =

3 m

,

13 m
(iv)
height =

7.66 m

, distances away =

4 m

,

14 m
(v)
height =

9.66 m

, distances away =

6 m

,

16 m

Question 12

12.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 70 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 45° and 60° respectively. Find the width of the river .

(i)

43.41 m
(ii)

45.41 m
(iii)

35.41 m
(iv)

37.41 m
(v)

40.41 m

Question 13

13.

The shadow of a vertical tower BA on a level ground is increased by 5 m, when the altitude of the sun changes from 60° to 30°. Find the height of the tower .

(i)

2.33 m
(ii)

5.33 m
(iii)

4.33 m
(iv)

6.33 m
(v)

3.33 m

Question 14

14.

A flagstaff stands on the top of a building at a distance of 35 m away from the foot of building . The angle of elevation of the top of the flagstaff is 60° and the angle of elevation of the top of the building is 45°. Find the height of the flagstaff .

(i)

(

105
2

√

2

−

35
2

√

6

)

m
(ii)

2450

m
(iii)

(

35

√

3

−

35

)

m
(iv)

(

35

√

18

−

35

√

6

)

m
(v)

(

2

−

√

3

)

m

Question 15

15.

From a point 130 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the pillar.

(i)

59.94 m
(ii)

49.94 m
(iii)

51.94 m
(iv)

57.94 m
(v)

54.94 m

Question 16

16.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 45° and the angle of elevation of the top of the building is 30°. If the height of the building is 6 m, find the height of the flag staff .

(i)

2.39 m
(ii)

4.39 m
(iii)

3.39 m
(iv)

5.39 m
(v)

6.39 m

Question 17

17.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 20 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the height of the other temple.

(i)

6.45 m
(ii)

7.45 m
(iii)

10.45 m
(iv)

8.45 m
(v)

9.45 m

Question 18

18.

A person, walking 20 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .

(i)

(

10

√

18

+

10

√

6

)

m
(ii)

200

m
(iii)

(

15

√

2

+

5

√

6

)

m
(iv)

(

2

+

√

3

)

m
(v)

(

10

√

3

+

10

)

m

Question 19

19.

A
building
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
building
is found to be
30°
.
If the height of the
building
is
160 m
,
find the distance between
the observation point and the foot of the
building
.

(i)

160

m
(ii)

160

√

3

m
(iii)

240

√

2

m
(iv)

480

m
(v)

160

√

18

m

Question 20

20.

An observer 1.3 m tall, is 130 m away from a tower . The angle of elevation of the top of the tower from her eyes is 30°. Find the height of the tower .

(i)

79.36 m
(ii)

81.36 m
(iii)

73.36 m
(iv)

76.36 m
(v)

71.36 m

Question 21

21.

From a point 200 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 45° respectively. Find the height of the cliff.

(i)

217.00 m
(ii)

184.00 m
(iii)

205.00 m
(iv)

183.00 m
(v)

200.00 m

Question 22

22.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
30°
.
If the distance between the point and the foot of the
chimney
is
160 m
,
find the height of the
chimney
.

(i)

160
3

m
(ii)

160

m
(iii)

160
3

√

18

m
(iv)

80

√

2

m
(v)

160
3

√

3

m

Question 23

23.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠c
(ii)

∠f
(iii)

∠e
(iv)

∠d

Question 24

24.

The angle of elevation of the top of a building from the foot of a tower is 60°. The angle of elevation of the top of the tower from the foot of the building is 30°. If the height of the tower is 90 m, find the height of the building .

(i)

251.98 m
(ii)

283.98 m
(iii)

255.98 m
(iv)

269.98 m
(v)

292.98 m

Question 25

25.

A man 1.3 m tall stands at a distance of 8.9 m from a lamp post and casts a shadow of 8.6 m on the ground. Find the height of the lamp post .

(i)

4.65 m
(ii)

0.65 m
(iii)

3.65 m
(iv)

2.65 m
(v)

1.65 m

Assignment Key